Finite Group Databasebeta

← C61×#25158 #29528591

Subgroups — C61×#25158 #29528591

Order 15616.

1140 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#463C211yesmaximal, characteristic, complemented
2C2×C61×#452C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic
4C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
5C61×#2426C211yesmaximal, characteristic, complemented
6C61×#2339C211yesmaximal, characteristic, complemented
7C61×#2066C211yesmaximal, characteristic, complemented
8C61×#2035C211yesmaximal, characteristic, complemented
9C61×#2034C211yesmaximal, characteristic, complemented
10C61×#2015C211yesmaximal, characteristic, complemented
11C61×#1968C211yesmaximal, characteristic, complemented
12C61×#1923C211yesmaximal, characteristic, complemented
13C61×#1879C211yesmaximal, characteristic, complemented
14C61×#1878C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×Q16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×SD16×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C2×#124×C61C2211yescharacteristic
22C2×C22⋊Q8×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×C4×Q8×C61C2211yescharacteristic
25C2×C4×D4×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#463—24no—
28C61×#452—24no—
29C61×#449—24no—
30C4×SD16×C61—24no—
31C2×#106×C61C2211yescharacteristic
32C2×#106×C61C2211yescharacteristic
33C2×C4⋊C8×C61C2211yescharacteristic
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#103×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×C22⋊C8×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C4×C8×C61C2211yescharacteristic
45C61×#396—21no—
46C61×#394—21no—
47C61×#391C2211yescharacteristic
48C61×#391C2211yescharacteristic
49C61×#390—21no—
50C61×#390C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#388—21no—
53C61×#386—21no—
54C61×#386—21no—
55C61×#381—21no—
56C61×#380C2211yescharacteristic
57C4×C22⋊C4×C61C2211yescharacteristic
58C2×#95×C61—21no—
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C22×Q8×C61C2311yescharacteristic
70C22×Q8×C61C2311yescharacteristic
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61C2311yescharacteristic
74C22×D4×C61C2311yescharacteristic
75C23×C4×C61—21no—
76C23×C4×C61—21no—
77C23×C4×C61—21no—
78C23×C4×C61C2311yescharacteristic
79C2×Q16×C61—22no—
80C2×Q16×C61—22no—
81C2×Q16×C61—41no—
82C2×SD16×C61—22no—
83C2×SD16×C61—22no—
84C2×SD16×C61—22no—
85C2×SD16×C61—22no—
86C2×SD16×C61—41no—
87C2×SD16×C61D414yescomplemented
88C2×D8×C61—22no—
89C2×D8×C61—22no—
90C2×D8×C61—22no—
91C22×C8×C61C2311yescharacteristic
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95#124×C61—22no—
96#124×C61—41no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—41no—
99#121×C61—22no—
100#121×C61—41no—
101C4×Q8×C61—22no—
102C4×Q8×C61—41no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—41no—
106C4×D4×C61—41no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61D411yescharacteristic
124C2×C22⋊C4×C61D411yescharacteristic
125C2×C42×C61—21no—
126C2×C42×C61C2311yescharacteristic
127C2×C42×C61C2311yescharacteristic
128#106×C61—22no—
129#106×C61—41no—
130C4⋊C8×C61—22no—
131#103×C61—22no—
132#103×C61—22no—
133#103×C61—22no—
134#103×C61—22no—
135#102×C61—22no—
136#102×C61—22no—
137#102×C61—41no—
138#102×C61D414yes—
139C22⋊C8×C61—22no—
140C22⋊C8×C61—22no—
141C4×C8×C61—22no—
142#95×C61—21no—
143#95×C61—21no—
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153#41×C61—44no—
154#41×C61—44no—
155#41×C61—44no—
156#41×C61—44no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C2×D412yes—
168C2×Q8×C61#4112yes—
169C2×D4×C61—24no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—81no—
184C2×D4×C61C2×D412yes—
185C2×D4×C61C2×D412yes—
186C2×D4×C61#4112yes—
187C22×C4×C61—24no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—42no—
201C22×C4×C61—42no—
202C22×C4×C61—42no—
203C22×C4×C61—42no—
204C22×C4×C61—42no—
205C22×C4×C61—42no—
206C22×C4×C61—81no—
207C22×C4×C61—81no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214Q16×C61—44no—
215SD16×C61—28no—
216SD16×C61—44no—
217D8×C61—44no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61C2×D412yes—
229C2×C8×C61C2×D412yes—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—42no—
238C4⋊C4×C61—42no—
239C4⋊C4×C61—81no—
240C4⋊C4×C61C2×D412yes—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—41no—
243C22⋊C4×C61—42no—
244C22⋊C4×C61—42no—
245C22⋊C4×C61—42no—
246C22⋊C4×C61—42no—
247C22⋊C4×C61—42no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—81no—
251C22⋊C4×C61—81no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61—42no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61C22×D411yescharacteristic
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—22no—
282Q8×C61—22no—
283Q8×C61—41no—
284Q8×C61—41no—
285Q8×C61—41no—
286Q8×C61—41no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—48no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—84no—
296D4×C61#12114yes—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—48no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—84no—
335C2×C4×C61—84no—
336C2×C4×C61#13512yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C8×C61—22no—
344C8×C61—22no—
345C8×C61—41no—
346C8×C61—41no—
347#25158C6111yesmaximal, characteristic, direct product factor, Sylow
348C22×C61—24no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61#52511yescharacteristic
370C22×C61D4211yescharacteristic
371C22×C61D4211yescharacteristic
372C22×C61C2×#13511yescharacteristic
373C22×C61#57511yescharacteristic
374C22×C61#57711yescharacteristic
375C22×C61#57711yescharacteristic
376C4×C61—22no—
377C4×C61—41no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—41no—
381C4×C61—42no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—81no—
385C4×C61—81no—
386C4×C61—81no—
387C4×C61C2×#12111yescharacteristic
388C4×C61#53811yescharacteristic
389C4×C61#54611yescharacteristic
390C4×C61#54611yescharacteristic
391C2×#463C2×C6111yescharacteristic, complemented
392C2×#452C2×C6111yescharacteristic, complemented
393C2×#449C2×C6111yescharacteristic
394C2×C4×SD16C2×C6111yescharacteristic, complemented
395#2426C2×C6111yescharacteristic, complemented
396#2339C2×C6111yescharacteristic, complemented
397#2066C2×C6111yescharacteristic, complemented
398#2035C2×C6111yescharacteristic, complemented
399#2034C2×C6111yescharacteristic, complemented
400#2015C2×C6111yescharacteristic, complemented
401#1968C2×C6111yescharacteristic, complemented
402#1923C2×C6111yescharacteristic, complemented
403#1879C2×C6111yescharacteristic, complemented
404#1878C2×C6111yescharacteristic, complemented
405#1864C2×C6111yescharacteristic, complemented
406C2×C61—44no—
407C2×C61—81no—
408C2×C61—161no—
409C2×C61#242411yescharacteristic
410C2×C61#310211yescharacteristic
411C2×C61#312511yescharacteristic
412C2×C61#326711yescharacteristic
413C2×C61#327511yescharacteristic
414C2×C61#328211yescharacteristic
415C2×C61#328411yescharacteristic
416C22×#41C22×C6111yescharacteristic
417C22×Q16C22×C6111yescharacteristic
418C22×SD16C22×C6111yescharacteristic
419C22×SD16C22×C6111yescharacteristic
420C22×D8C22×C6111yescharacteristic
421C2×#124C22×C6111yescharacteristic
422C2×C22⋊Q8C22×C6111yescharacteristic
423C2×#121C22×C6111yescharacteristic
424C2×C4×Q8C22×C6111yescharacteristic
425C2×C4×D4C22×C6111yescharacteristic
426C2×C4×D4C22×C6111yescharacteristic
427#463—24no—
428#452—24no—
429#449—24no—
430C4×SD16—24no—
431C2×#106C22×C6111yescharacteristic
432C2×#106C22×C6111yescharacteristic
433C2×C4⋊C8C22×C6111yescharacteristic
434C2×#103C22×C6111yescharacteristic
435C2×#103C22×C6111yescharacteristic
436C2×#103C22×C6111yescharacteristic
437C2×#103C22×C6111yescharacteristic
438C2×#102C22×C6111yescharacteristic
439C2×#102C22×C6111yescharacteristic
440C2×#102C22×C6111yescharacteristic
441C2×#102C22×C6111yescharacteristic
442C2×C22⋊C8C22×C6111yescharacteristic
443C2×C22⋊C8C22×C6111yescharacteristic
444C2×C4×C8C22×C6111yescharacteristic
445#396—21no—
446#394—21no—
447#391C22×C6111yescharacteristic
448#391C22×C6111yescharacteristic
449#390—21no—
450#390C22×C6111yescharacteristic
451#389C22×C6111yescharacteristic
452#388—21no—
453#386—21no—
454#386—21no—
455#381—21no—
456#380C22×C6111yescharacteristic
457C4×C22⋊C4C22×C6111yescharacteristic
458C2×#95—21no—
459#340C22×C6111yescharacteristic
460#340C22×C6111yescharacteristic
461#336C22×C6111yescharacteristic
462#336C22×C6111yescharacteristic
463C61#2515811yescharacteristic, direct product factor, Sylow
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—41no—
469C2×#41—41no—
470C22×Q8C23×C6111yescharacteristic
471C22×Q8C23×C6111yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C23×C6111yescharacteristic
475C22×D4C23×C6111yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4C23×C6111yescharacteristic
480C2×Q16—22no—
481C2×Q16—22no—
482C2×Q16—41no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—41no—
488C2×SD16D4×C6114yescomplemented
489C2×D8—22no—
490C2×D8—22no—
491C2×D8—22no—
492C22×C8C23×C6111yescharacteristic
493C22×C8C23×C6111yescharacteristic
494C22×C8C23×C6111yescharacteristic
495C22×C8C23×C6111yescharacteristic
496#124—22no—
497#124—41no—
498C22⋊Q8—22no—
499C22⋊Q8—41no—
500#121—22no—
501#121—41no—
502C4×Q8—22no—
503C4×Q8—41no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—41no—
507C4×D4—41no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4C23×C6111yescharacteristic
512C2×C4⋊C4C23×C6111yescharacteristic
513C2×C4⋊C4C23×C6111yescharacteristic
514C2×C4⋊C4C23×C6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4D4×C6111yescharacteristic
525C2×C22⋊C4D4×C6111yescharacteristic
526C2×C42—21no—
527C2×C42C23×C6111yescharacteristic
528C2×C42C23×C6111yescharacteristic
529#106—22no—
530#106—41no—
531C4⋊C8—22no—
532#103—22no—
533#103—22no—
534#103—22no—
535#103—22no—
536#102—22no—
537#102—22no—
538#102—41no—
539#102D4×C6114yes—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C4×C8—22no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95D4×C6111yescharacteristic
550#95D4×C6111yescharacteristic
551C24—21no—
552C24—21no—
553C24C2×D4×C6111yescharacteristic
554#41—44no—
555#41—44no—
556#41—44no—
557#41—44no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C2×D4×C6112yes—
569C2×Q8#41×C6112yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—81no—
585C2×D4C2×D4×C6112yes—
586C2×D4C2×D4×C6112yes—
587C2×D4#41×C6112yes—
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C6111yescharacteristic
610C22×C4C2×D4×C6111yescharacteristic
611C22×C4C2×D4×C6111yescharacteristic
612C22×C4C2×D4×C6111yescharacteristic
613C22×C4C2×D4×C6111yescharacteristic
614C22×C4C24×C6111yescharacteristic
615Q16—44no—
616SD16—28no—
617SD16—44no—
618D8—44no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8C2×D4×C6112yes—
630C2×C8C2×D4×C6112yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C4⋊C4C2×D4×C6112yes—
642C22⋊C4—22no—
643C22⋊C4—41no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—42no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23C22×D4×C6111yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—48no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697D4#121×C6114yes—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—48no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4#135×C6112yes—
738C2×C4C22×D4×C6111yescharacteristic
739C2×C4C22×D4×C6111yescharacteristic
740C2×C4C2×#41×C6111yescharacteristic
741C2×C4C2×#41×C6111yescharacteristic
742C2×C4H(5,𝔽2)×C6111yescharacteristic
743C2×C4H(5,𝔽2)×C6111yescharacteristic
744C8—22no—
745C8—22no—
746C8—41no—
747C8—41no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C61×#52511yescharacteristic
770C22D42×C6111yescharacteristic
771C22D42×C6111yescharacteristic
772C22C2×#135×C6111yescharacteristic
773C22C61×#57511yescharacteristic
774C22C61×#57711yescharacteristic
775C22C61×#57711yescharacteristic
776C4—22no—
777C4—41no—
778C4—42no—
779C4—42no—
780C4—41no—
781C4—42no—
782C4—41no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4C2×#121×C6111yescharacteristic
788C4C61×#53811yescharacteristic
789C4C61×#54611yescharacteristic
790C4C61×#54611yescharacteristic
791C2—44no—
792C2—81no—
793C2—161no—
794C2C61×#242411yescharacteristic
795C2C61×#310211yescharacteristic
796C2C61×#312511yescharacteristic
797C2C61×#326711yescharacteristic
798C2C61×#327511yescharacteristic
799C2C61×#328211yescharacteristic
800C2C61×#328411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C61×#463C2semidirect
2. C2×C61×#452C2semidirect
4. C2×C4×SD16×C61C2semidirect
5. C61×#2426C2semidirect
6. C61×#2339C2semidirect
7. C61×#2066C2semidirect
8. C61×#2035C2semidirect
9. C61×#2034C2semidirect
10. C61×#2015C2semidirect
11. C61×#1968C2semidirect
12. C61×#1923C2semidirect
13. C61×#1879C2semidirect
14. C61×#1878C2semidirect
15. C61×#1864C2semidirect
87. C2×SD16×C61D4semidirect
347. #25158C61direct (N × H)
391. C2×#463C2×C61semidirect
392. C2×#452C2×C61semidirect
394. C2×C4×SD16C2×C61semidirect
395. #2426C2×C61semidirect
396. #2339C2×C61semidirect
397. #2066C2×C61semidirect
398. #2035C2×C61semidirect
399. #2034C2×C61semidirect
400. #2015C2×C61semidirect
401. #1968C2×C61semidirect
402. #1923C2×C61semidirect
403. #1879C2×C61semidirect
404. #1878C2×C61semidirect
405. #1864C2×C61semidirect
463. C61#25158direct (N × H)
488. C2×SD16D4×C61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C61×#4632
C2×C61×#4522
C2×C61×#4492
C2×C4×SD16×C612
C61×#24262
C61×#23392
C61×#20662
C61×#20352
C61×#20342
C61×#20152
C61×#19682
C61×#19232
C61×#18792
C61×#18782
C61×#18642
#2515861